It's very interesting the way you laid out the conditions for Papal Infallibility. It's similar to the way one would list the elements in a legal statute. For instance, the elements necessary for the crime of robbery might be:

A person is guilty of robbery when,
1. They intentionally
2. take what belongs to another person
3. by force
4. or threat of force

I've found in my legal studies that breaking down statutes helps to clarify what's necessary for the actual commission of a crime. I think it is also very helpful in understanding the necessary elements for Catholic teaching.